Constraint satisfaction appear everywhere. With CSPs being ubiquitous, it is worth developing specialized techniques for solving them. Some powerful techniques have been developed, to exploit the characteristics of CSPs. If you want to make use of these techniques, you need to cast a problem as a CSP. This step is called problem formulation, or modelling.
Problem formulation is more an art than a science. There is no mechanical way to generate a CSP. But you can approach it by using a check list.
Once you have formulated your CSP, you should be able to ignore the original specification when you solve the problem. You can check whether your formulation is correct by asking yourself: